Inversion formulas for cone transforms arising in application of Compton cameras

It has been suggested that a Compton camera should be used in single photon emission computed tomography because a conventional gamma camera has low efficiency. It brings about a cone transform, which maps a function onto the set of its surface integrals over cones determined by the detector position, the central axis, and the opening angle of the Compton camera. We provide inversion formulas using complete Compton data for three- and two-dimensional cases. Numerical simulations are presented to demonstrate the suggested algorithms in dimension two. Also, we discuss other inversions and the stability estimates of a cone transform with a fixed central axis.